![](media/image1.png){width="5.0in" height="0.6in"}**U. S. Geological
Survey Open-File Report 98-767, Paper Edition, Updated July 21, 1999**

**TABLE-TOP EARTHQUAKES\
A Demonstration of Seismology for Teachers and Students that can be used
to Augment Lessons in:**

**Earth Science\
**Faulting\
Elastic Rebound\
Plate Motions

**Physics\
**Forms of Energy\
Elasticity\
Friction\
Magnetism\
Waves

**Math\
**Graphing\
Logarithms\
Probability

**Social Studies\
**Hazard Mitigation

**Geography\
**Global Distribution of Earthquakes

**By John C. Lahr\
Denver Federal Center\
Box 25946, Mail Stop 966\
Denver, CO 80225\
Phone: (303) 273-8596\
Email: <lahr@usgs.gov>**

**Open-file Report 98-767,**

**On-Line Edition is located at**
[[http://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-98-0767/]{.underline}](http://lahr.org/john-jan/tabletop)**\
This document is:**
[[http://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-98-0767/tabletop.doc]{.underline}](http://lahr.org/john-jan/tabletop/tabletop.doc)\
This report is preliminary and has not been edited or reviewed for
conformity with U.S. Geological Survey (USGS) editorial standards. Any
use of trade, product, or firm names is for descriptive purposes only
and does not imply endorsement by the U.S. Government.

**Summary**

The apparatus consists of a heavy object that is dragged steadily with
an elastic cord. Although pulled with a constant velocity, the heavy
object repeatedly slides and then stops. A small vibration sensor,
attached to a computer display, graphically monitors this intermittent
motion.

This intermittent sliding motion mimics the intermittent fault slippage
that characterizes the earthquake fault zones.  In tectonically active
regions, the Earth\'s outer brittle shell, which is about 50 km thick,
is slowly deformed elastically along active faults.   As the deformation
increases, stress also increases, until fault slippage releases the
stored elastic energy. This process is called *elastic rebound*.

Detailed instructions are given for assembly and construction of this
demonstration.   Included are suggested sources for the vibration sensor
(geophone) and the computer interface. Exclusive of the personal
computer, the total cost is between \$125 and \$150.

I gave a talk at the Geological Society of America\'s Cordilleran
Section Centennial meeting on June 2, 1999. The slides show how this
table-top demonstration can be used to help meet many of the K-12
teaching goals described in Benchmarks for Science Literacy (American
Association for the Advancement of Science, 1993).

  **Construction of Earthquake Machine**

Read through this and the Setup and Operation sections before purchasing
any equipment, as some trouble-shooting alternatives are offered.

**Materials for rock-slide:**

*Base for rock-slide*: 3\' 5\" of 1\"x6\" pine\
*Sides for rock-slide*: 3\' of 1\"x2\" pine\
*Stop for rock slide*: 7\" of 1\"x2\" pine\
*Elastic shock cord*: 15\" long by 1/4\" diameter\
*Rock with a flat side, or a brick*\
*Rough sand paper to cover base of rock or brick*:  may be required to
get best sliding properties.\
*Non-elastic cord*: 10\'\
*Three C-clamps*: One to clamp the winch to one table and two to clamp
the rock-slide to another table.\
*Screws: * 10 with a length of  1 1/4\"  

**Materials for winch:**

*1 13\" length of 3/4\" PVC pipe, cut into 3 pieces with lengths of 7\",
3\", and 3\"\
2 90 degree PVC junctions\
1 straight PVC junction\
PVC cement\
1 2\"x4\" (wood) 1\' in length\
2 pieces of 1\"x6\" wood cut 8\" long\
4 2 1/2 \" long wood screws*

**Materials for seismic display:**

*Geophone*: A small 8 to 14 Hz vertical exploration geophone may be
purchased from some surplus stores. For example: All Electronics
Corporation, (800) 826-5432,  <http://www.allcorp.com/>,  currently
(November 1998) sells their catalog number GP-1 geophone for \$8.  Also
Arlen Juels of Seistex \'86 Inc. has a number of used exploration
geophones that he is willing to provide to teachers for the cost of
shipping. He can be contacted at ajuels@seistex.com.

*Analog to digital converter (AD) and display software*: The least
expensive AD unit that I have been able to find is Dataq\'s DI-150-SP,
which sells for \$100. This unit attaches to a PC serial port and
includes software for MS Windows that will display the seismic data in
real time. Dataq Instruments (888) 666-2907; 
[http://www.dataq.com](http://www.dataq.com/).  

**Assembly**

Using 1 1/4\" screws, attach the sides and stop to the rock-slide base,
as indicated in the diagram below.

![](media/image2.png){width="4.141666666666667in"
height="1.4666666666666666in"}

Drill a 1\" diameter hole in each of the 1\"x6\" boards.   The center of
the holes should be 1 3/4\" from the 6\" edge of the wood, as indicated
in the sketch below.  Using the four 2 1/2\" wood screws, attach the
sides of the winch to the 2\"x4\" base.  The extra length on the base is
to allow more room for clamping the winch to a table.  Using PVC cement,
attach the three pieces of PVC together using the two 90-degree
junctions, as indicated.  Then slide the 7\"-long pipe through the two
holes in the winch.  If the pipe does not slide easily in the holes, use
a round file to enlarge the holes.  Glue a straight PVC junction to the
end of the 7\"-long pipe to keep it from sliding out of the winch.  
Drill a 1/4\" diameter hole through one side of  the 7\" section of PVC
pipe.  Feed one end of the  non-elastic cord through this hole and tie a
knot in the end so that the cord will be securely attached to the pipe.

![](media/image3.png){width="1.6833333333333333in"
height="1.4583333333333333in"}

Using the C-clamps, secure the winch to one table and the rock-slide to
an adjacent table. The use of  two tables prevents the winch from
vibrating the table on which the geophone is located. 

Securely attach a loop of non-elastic cord to the rock or brick, leaving
an open loop on one dangling end of the cord. Wind the rest of the
non-elastic cord onto the winch. Secure one end of the 15\" piece of
elastic shock cord to the winch cord and the other to the dangling end
of the cord attached to the brick or rock.

![](media/image4.png){width="6.116666666666666in"
height="2.283333333333333in"}   

**Setup and Operation**

Set up the geophone and display computer on the table with the
rock-slide. The geophone does not have to be on or right next to the
rock-slide. In fact, it is better to have it a few feet away so that it
is clear that the vibrations from the sliding rock must travel some
distance along the tabletop to reach the sensor. Adjust the display
software so that the trace is scrolling on the screen and a slight tap
on the table is clearly registered.  

The distance between the winch and the rock-slide should be adjusted so
that the shock cord does not begin to wind onto to winch; this maintains
a constant elastic component during the entire travel of the rock or
brick.  Next try pulling the rock or brick along with the winch.  The
speed should be such that it takes 30 seconds to a minute to move the
entire length of the rock-slide.  If it slides steadily rather than in
discrete events (earthquakes), an adjustment is necessary.  Try
increasing the friction or using a longer or more stretchy section of
shock cord.  Friction can be increased by gluing coarse sandpaper to the
sliding surface of the rock or brick, by using a heavier rock, or by
using two bricks, one on top of the other.  If the rock slips too far in
one event, such as more than half of  the entire length of the
rock-slide, then decrease the weight of the rock, decrease the length of
the elastic cord, or use a less stretchy elastic cord.

When the adjustments are complete, the rock should generate
approximately 4 to 10 events per run, and each of these \"earthquakes\"
should be clearly registered on the computer screen display (the
seismogram).

**Earth Science**

Most of the Earth\'s processes are slow, but steady. This makes them
difficult to comprehend, because little seems to happen on a human time
scale. Mountains are slowly uplifted and even more slowly eroded away;
rivers slowly cut gorges and transport sediments to growing deltas, but
the pace is so slow that even after many generations little seems to
have changed. Earthquakes are an exception; they involve rapid enough
slippage on a fault to cause waves of vibrations to be radiated outward.
The vibrations can be felt and, if the fault intersects the surface of
the earth, the resulting displacement can be observed directly.

**Plate Tectonics.**  Plate tectonics is the study of the consequences
of the slow motion between the plates that make up the outer shell of
the earth.  There are about a dozen major plates and they are about 50
km thick.  The temperature and material properties at the base of the
plates are such that they can slip steadily without producing any
earthquakes.  However, when a plate itself is deformed, due to mountain
building, for example, or when one plate must slide past another,
earthquakes are produced.  For years, and in some cases as much as many
hundreds of years, very little slip may occur across a portion of one of
the boundaries between two plates that are in relative motion with
respect to each other.  During this time both plates are deformed and
bent elastically near the boundary, and all the while the stress in the
region is increasing.  Eventually, during an earthquake, the plates
quickly slide past one another and the stress is greatly reduced.  This
process of slow deformation followed by rapid release is called *elastic
rebound* and was first proposed by H. F. Reed following studies of the
1906 San Francisco earthquake.

The following figure by USGS seismologist Will Prescott schematically
illustrates a fence crossing the San Andreas fault in California.  The
figure is from the web page 
<http://quake.wr.usgs.gov/more/1906/reid.html>.

 ![](media/image5.png){width="4.225in" height="3.341666666666667in"}

An excellent tutorial on earthquakes, which was developed by the
Southern California Earthquake Center, is available at 
<http://www.scecdc.scec.org/Module/> .  Although aimed at high school
and undergraduate levels, this module would also be a good source of
information for middle school students who wanted to learn more about
this subject.  Especially helpful are the animations of the various
types of faulting.

**Hazards.** The vibrations from large earthquakes can be strong enough
and last long enough to be a serious hazard. They can cause man-made
structures such as buildings and bridges to collapse and they can cause
ground failures such as landslides. If an earthquake produces rapid
deformation of a body of water, be it uplift of the floor of the ocean
or movement of a lake or fjord, a large and potentially deadly wave of
water can be generated.  When in the ocean, a wave of this sort is
called a tsunami wave, whereas in a smaller body of water it is called a
seiche.  A small dish of water places on the table with the rock-slide
will show small ripples following an \"earthquake,\" analogous to the
waves that could be generated in a lake.

**Waves in the solid Earth.** Some of the seismic waves  generated by
earthquakes are confined to the outermost layers of the earth (surface
waves), somewhat like the ripples that travel outward on the surface of
a pond from the point where a rock has hit the water. Other waves (body
waves) travel outward in all directions, including straight down through
the center of the earth. Much of what is known about the inside of the
earth was learned from the study of the waves generated by earthquakes.

**Compressional and Shear Waves.** The three most common states of any
material are solid, liquid, and gas. A material in any of these three
states will resist having its volume changed by being squeezed or
stretched. A compressional wave, such as a sound wave in air, consists
of a series of compressions and stretches (called dilations) of the air
as the sound travels outward from the source. Compressional waves can
also travel in a liquid or a solid. In a compressional wave, the back
and forth motion of the material is in the same direction as the wave is
traveling.

The figure below shows a compressional wave traveling to the right.  
The material is alternatively compressed and expanded from its resting
state as the wave passes through.

![](media/image6.png){width="3.125in" height="1.2166666666666666in"}

Of the three states, solids are the only one that will, upon being bent,
return to their original shape. Another way to say this is that solids
resist shearing.   The diagram below illustrates the difference between
shear and compression.

![](media/image7.png){width="5.608333333333333in"
height="3.2416666666666667in"}

 Unlike liquids or gasses, solids can transmit waves that involve back
and forth motion of the material perpendicular to the direction that the
wave is traveling.  The figure below shows a shear wave traveling to the
right.  Note that the material is moving in and out of the page,
perpendicular to the direction of wave travel.

![](media/image8.png){width="3.2916666666666665in"
height="1.8166666666666667in"}

A slinky may to used to demonstrate both compressional and shear waves,
which can be seen traveling along the length of the slinky. 
Compressional waves are generated if one end of a stretched slinky is
pushed quickly along the axis of the slinky and shear waves are
generated if one end is displaced quickly in a direction perpendicular
to the axis of the slinky.

![](media/image9.png){width="4.025in" height="2.6in"}

 

**Physics**

**Energy, friction and waves. ** It is interesting to consider the flow
of energy that is involved in making the rock-slide.  Chemical energy
from one\'s muscles is first used to turn the winch handle.  At first
the rock does not move, so the energy is stored in the elastic cord. 
The more the elastic cord is stretched, the more energy is stored within
it, and the greater the force on the rock.  When the **static friction**
that is holding the rock in place is exceeded, the rock will start
sliding.  Because **sliding friction** is less than static friction, the
rock will continue sliding some distance until the force from the
elastic cord is equal to the sliding friction that is resisting motion
of the rock.  The energy that was slowly stored up within the elastic
cord is quickly released and converted into kinetic energy of the moving
rock.  As the rock slides along, its kinetic energy is dissipated by
heating up the sliding surfaces and by radiating energy in the form of
**elastic waves**.  The seismograph detects these elastic waves as they
pass by, and they are displayed on the seismogram.  

**Magnetism. ** The geophone works by magnetic induction, which is the
term for the generation of a voltage within a conductor that is
subjected to a varying magnetic field.  A geophone consists of a coil of
wire suspended by a spring.  A strong magnet is attached to the
geophone\'s case, so when the coil vibrates up and down on its spring it
is moving with respect to the magnetic field of the magnet.  This motion
of the coil with respect to the magnetic field generates a voltage, and
it is this voltage that is displayed on the seismogram.

A very simple geophone can easily be made by winding magnet wire on a
small plastic cylinder, which is then mounted vertically.  An old
marking pen can be cut up to make the plastic tube.  One end of a
4-inch-long piece of rubber from a rubber band is attached to a magnet
that is just small enough to slide freely within the plastic cylinder. 
The other end of the rubber band is attached to a mounting point
directly above the cylinder. 

![](media/image10.png){width="3.158333333333333in"
height="3.2333333333333334in"}

Any vibration will cause the magnet to bounce up and down within the
coil and will produce a small voltage in coil wire.  To see how the
homemade geophone is working, it can be attached to the AD and computer
display in place of the commercial geophone.  Although not as sensitive,
this illustrates the principal of how a geophone works.  It is best to
use a strong magnet, such as a rare-earth magnet, so that even a slight
motion of the magnet will generate a detectable voltage.  Sources of
strong magnets include Radio Shack and All Electronics Corporation,
(800) 826-5432,   <http://www.allcorp.com/>.

**Math**

**Graphing**.  The seismogram that is displayed on the PC\'s screen is a
graph of the voltage produced by the geophone as a function of time. 
The voltage is proportional to the velocity of the coil with respect to
the magnet, and for frequencies higher than the natural frequency of the
geophone this voltage will be proportional to the vertical velocity of
the table at the location of the geophone.   Another time graph that the
students may be more familiar with is the stock market average selling
price versus time. 

**Logarithms**.  In seismology, the energy of the vibrations produced by
an earthquake can vary enormously.  The total energy of the seismic
waves generated by the  smallest earthquake that could be located by a
local network of seismometers is about 2,000 joules (J).  The largest
earthquake ever recorded released 11,200,000,000,000,000,000 J of energy
as seismic waves and was observed on seismometers all around the World. 
As you can imagine, it is not very convenient dealing with numbers that
have such a large range.  On the Richter magnitude scale, the magnitude
of a 2,000 J event is minus 1.0 while the magnitude of the largest
recorded earthquake was 9.5.  The relationship between earthquake energy
and magnitude is said to be logarithmic because the equation relating
energy and magnitude includes a logarithmic term. 

For energy, E, in joules, the equation is:   log E = 1.5 M + 4.8  (this
is log to the base 10).\
Or expressed another way:   E = 10 raised to the power (1.5 M + 4.8)\
Or:  Magnitude, M = (log E - 4.8)/1.5

Note that this indicates that an increase of one unit of magnitude
results in 32 times greater energy release.

\<div align=\"center\"\>

  ------------ ------------ ------------------ -------------------------------------
  Earthquake                                   
  Energy as a                                  
  Function of                                  
  Magnitude                                    

  Magnitude    Energy       Energy in joules\  Notes
               Equivalent   (1 J = 1 newton    
               Weight of    meter)             
               TNT\*                           

  -3.0         0.001 ounces 2 J                1.5 foot pounds (18 inch pounds)

  -2.0         0.032 ounces 63.1 J             47 foot pounds

  -1.0         1.0 ounces   2E+03 J            1,500 foot pounds

  0.0          32 ounces    63.1E+03 J          

  1.0          63 pounds    2E+06 J             

  2.0          1 ton        63.1E+06 J         Only felt nearby.

  3.0          32 tons      2E+9 J              

  4.0          1 kton       63.1E+9 J          Often felt up to 10\'s of miles away.

  5.0          32 ktons     2E+12 J             

  6.0          1,000 ktons  63.1E+12 J          

  6.9          22,700 ktons 1.41E+15 J         1995 Kobe, Japan, Earthquake

  7.0          32,000 ktons 2E+15 J             

  8.0          1 Mtons      63.1E+15 J          

  9.0          32,000 Mtons 2E+18 J             

  9.2          64,000 Mtons 3.98E+18 J         1964 Alaska Earthquake - Second
                                               largest instrumentally recorded
                                               earthquake

  9.5          180,000      11.2E+18 J         1960 Chile - Largest instrumentally
               Mtons                           recorded earthquake
  ------------ ------------ ------------------ -------------------------------------

\</div\>

\*This is the approximate amount of TNT that would be required to
generate high-frequency seismic waves of similar amplitude to those from
an earthquake of each magnitude.  This is based on the observation that
a 1-kton explosion is approximately equivalent to a magnitude 4
earthquake (Evernden and others, 1986).

**Computing Magnitude**.  The magnitude of the small \"earthquakes\"
generated by the sliding rock can be computed if we know the energy
released during the event.  The force times the distance gives the
energy.  If a small fish scale is linked into the cord, between the
winch and the sliding rock, then the force on the rock can be measured. 
If the distance of that the rock slides is also measured, then the
energy can be computed, and from the energy the magnitude can be
determined.  (For this exercise we will ignore the portion of the energy
that goes into heating the rock and the board due to friction and assume
that all of the energy goes into seismic waves.)  The units of inches of
distance and pounds of force are not usually used in scientific
investigations today, as the International System (SI) is almost
exclusively used.  In the SI system the unit of distance is the meter (1
m = 39.37 inches) and the unit of force is the newton (1 N = 0.225
pounds of force).   However, because fish scales are usually not
calibrated in newtons, and using a mixed English and metric system such
as centimeter pounds seems a bit awkward at best, inch pounds are used
in following table and graph.  For more information on the SI system of
units, see Dr. Russ Rowlett\'s web site at the University of North
Carolina, <http://unc.edu/~rowlett/units/sipm.html>

\<div align=\"center\"\>

  ----------------- ----------------- ----------------- -----------------
  Table of                                              
  magnitude versus                                      
  energy for the                                        
  range 1 to 100                                        
  inch pounds.                                          

  1 -3.83\          26 -2.89\         51 -2.69\         76 -2.58\
  2 -3.63\          27 -2.88\         52 -2.69\         77 -2.57\
  3 -3.51\          28 -2.87\         53 -2.68\         78 -2.57\
  4 -3.43\          29 -2.86\         54 -2.68\         79 -2.57\
  5 -3.37\          30 -2.85\         55 -2.67\         80 -2.56\
  6 -3.31\          31 -2.84\         56 -2.67\         81 -2.56\
  7 -3.27\          32 -2.83\         57 -2.66\         82 -2.56\
  8 -3.23\          33 -2.82\         58 -2.66\         83 -2.55\
  9 -3.20\          34 -2.81\         59 -2.65\         84 -2.55\
  10 -3.16\         35 -2.80\         60 -2.65\         85 -2.55\
  11 -3.14\         36 -2.79\         61 -2.64\         86 -2.54\
  12 -3.11\         37 -2.79\         62 -2.64\         87 -2.54\
  13 -3.09\         38 -2.78\         63 -2.63\         88 -2.54\
  14 -3.07\         39 -2.77\         64 -2.63\         89 -2.53\
  15 -3.05\         40 -2.76\         65 -2.62\         90 -2.53\
  16 -3.03\         41 -2.76\         66 -2.62\         91 -2.53\
  17 -3.01\         42 -2.75\         67 -2.61\         92 -2.52\
  18 -2.99\         43 -2.74\         68 -2.61\         93 -2.52\
  19 -2.98\         44 -2.74\         69 -2.61\         94 -2.52\
  20 -2.96\         45 -2.73\         70 -2.60\         95 -2.51\
  21 -2.95\         46 -2.72\         71 -2.60\         96 -2.51\
  22 -2.94\         47 -2.72\         72 -2.59\         97 -2.51\
  23 -2.92\         48 -2.71\         73 -2.59\         98 -2.50\
  24 -2.91\         49 -2.70\         74 -2.59\         99 -2.50\
  25 -2.90          50 -2.70          75 -2.58          100 -2.50
  ----------------- ----------------- ----------------- -----------------

\</div\>

![](media/image11.jpeg){width="6.489583333333333in"
height="5.014583333333333in"}

**Probability.** Predicting when the rock will slide is similar to the
problem of predicting when an earthquake will occur.  A very long-term
prediction would be, assuming that the winch is turned steadily, that
earthquakes will eventually take the rock from one end of the board to
the other.  A similar prediction, often called a forecast if it is not
related to a specific earthquake at a specific time, would be that
earthquakes will continue to occur on the San Andreas fault as long the
Pacific Plate continues to move northwestward with respect to the North
American plate.   In California, the San Andreas fault is the boundary
between these plates.   One can also say in a qualitative way that the
longer it has been since an earthquake has occurred on an active fault,
the higher the probability that it will occur within the next interval
of time.  This is clear in the table-top earthquake demonstration
because one can see the elastic cord stretch and thus increase the force
on the rock.   In a similar way today, global positioning satellite
(GPS) measurements are being made of the deformation of the ground
surface in areas such as California.  If these measurements are
continued for decades they will allow scientists to gauge which areas
have been strained the most, and are therefore the most likely to
experience earthquakes.

**Social Studies**

**Hazard Mitigation**.  Many areas of the United States have the
potential of experiencing a damaging earthquake.  It is interesting to
discuss the way society deals with this and other hazards.  Are these
issues that should be left to each individual, or is there a role for
common action through governmental regulations?   How safe is your
school?  Your home?  There is a lot

of information available from the Federal Emergency Management Agency
(FEMA), including this page especially for kids: 
<http://www.fema.gov/kids/quake.htm>  

**Geography**

**Global Distribution of Earthquakes**.  An interesting project
involving both geography and seismology is to plot the earthquakes that
are located around the world for a few months.  This requires a large
map of the world and internet access.  Each school day print out the
list of earthquakes from this USGS web site:    
<http://wwwneic.cr.usgs.gov/neis/finger/quake>

For each earthquake place a colored stick-on dot on the map at the
location indicated.   Use red for earthquakes less than 50 km deep,
orange for earthquakes between 51 and 150 km deep and yellow for even
deeper events.  After a period of some months, the global pattern of
earthquakes will be clearly indicated on the map.  Keep a list of all of
the countries effected, and for an added challenge try to find the word
for earthquake in the language of each country. 

The pattern of colors will reveal the zones where an oceanic plate has
slid under an adjacent plate and extends deep into the Earth.  Note that
these zones also have active volcanoes.  An excellent publication that
describes the relationships between plate motions, volcanoes, and the
structure of the Earth is on the web site: 
<http://pubs.usgs.gov/publications/text/dynamic.html>

**Acknowledgements**

I am grateful for very helpful reviews of this report by Ed Cranswick
and Susan Rhea.  In addition, I thank Ross Stein for demonstrating the
basic idea of using an elastic cord and a rock as an analog for
earthquake faulting.

**References**

Evernden, J.F., Archambeau, C.B., and Cranswick, E., 1986, An evaluation
of seismic decoupling and underground nuclear test monitoring using
high-frequency seismic data, **Reviews of Geophysics**, v. 24, no. 2, p.
143-215

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