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U.S. Geological Survey Open-File Report 98–767

Pubs Warehouse

# Table-Top Earthquakes

#### By John C. Lahr

##### 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

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| -  **Report** PDF file (324 kB)  PDF Version.

**On-line Version 2.0**

Posted March 2001; revised March 2011More info: http://earthquake.usgs.gov/

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. |
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### 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. 

### 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.allcomp.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.   

**Assembly**

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

    

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. 

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. 

    

### 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 stretchier 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.

  

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.

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.

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.

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.

 

### 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.  

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.allcomp.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.

 

| Earthquake Energy as a Function of Magnitude |
|----------------------------------------------|
| Magnitude                                    | Energy Equivalent Weight of TNT* | Energy in joules    (1 J = 1 newton meter) | Notes |
| -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                                          | 1,000 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 Mtons | 11.2E+18 J | 1960 Chile - Largest instrumentally recorded earthquake |

 

*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

 

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

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:  https://pubs.usgs.gov/gip/dynamic/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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