## 7. Modeling Earthquakes in the Classroom Using a Mechanical Fault Model

#### Introduction:

In this exercise, you will explore the behavior of faults, how earthquakes occur, and the challenges of earthquake prediction.

The exercise is based on an activity developed by Hall-Wallace (1998) in which the mechanics of faults is investigated using an apparatus that simulates earthquakes on a desktop. The experimental apparatus includes: blocks of wood that are placed on a flat board and connected to a bungee cord and a rope wrapped around a hand crank (Figure 1). The geological motion of “tectonic plates” is modeled by slowly turning the crank, and “earthquakes” (actually “blockquakes”) are modeled as events in which the block slips. Fault friction is modeled by using different types of sandpaper between the blocks and the board.

Experimental Setup:

Your team should have the apparatus shown in Figure 1.

 Figure 1: Experimental Apparatus for the “blockquake” exercise.

The block(s) are placed on the board and attached to a spring scale (Force Meter). The block and Force Meter are connected to the bungee cord, and the Force Meter is then connected to the non-elastic rope attached to the metal crank. Start the block at zero cm on the meter stick, and write down the mass of the block and the position of the block on the board before you move anything.

Assign the following roles to your team members, and rotate roles throughout the experiment so that each participant gets a chance to play each role:

• Magnitude Recorder: This person records the magnitude of each “blockquake”. For this experiment, we will consider the amount the blocks move during each blockquake to be the “magnitude” of that blockquake (M). You will record this information under the Magnitude column on your data sheet.
• Force Recorder: This person will record the amount of force on the Force Meter before and after each “blockquake”. You will record your information in the Fbefore and Fafter columns of your data sheet.
• Energy Recorder: This person will record the number of cm that the rope moves through the rope guide as the rope is cranked by the person operating the hand crank (by counting the number blue tick marks on the rope that moves through the rope guide). You will record your data in the Energy (E) column of your data sheet. This value represents the amount of energy stored in the stretched bungee cord.
• Energy Generator: This person turns the hand crank to add energy. This person needs a steady hand.

Note that we have simplified the concept of energy here by only recording the amount that the bungee cord is stretched (x). The actual energy is (1/2)kx2 (where k is the “spring constant” of the bungee cord”).

Data You Will Collect and Record on the Data Sheets:

M = mass of the block (grams)
A = “fault area” = length times width of the block’s bottom surface (in square centimeters)
Fbefore = force on the scale when the block first begins to move
Fafter = force on the scale when the block comes to rest
Fbefore – Fafter = change in stress (actually force) due to release of energy. (Note: Stress is force per unit area on the fault surface, and since area of the block surface is a constant in this experiment, we use the terms stress and force interchangeably in this exercise.)
Magnitude (M) = amount the blocks move during the blockquake
“Stored energy” (E) = length of the string passing through the rope guide before the blockquake occurs (number of blue tick marks on the rope that moves through the rope guide)

All forces are measured in Newtons (N). 1 N = 0.22 lb, which is about the weight of one apple.

Experimental Procedure:

1. Determine the mass of the blocks (adding the mass of the blocks together if you have more than one). Two or three blocks are recommended. Record the number of blocks and their mass on your data sheets.
2. Start the front or the back of your blocks at the 0 mark of meter stick.
3. Begin conducting the experiment. Each team member should record the data they are responsible for collecting, and then at the end of the experiment you will share your data with your teammates.
4. After recording the block’s mass and position, begin turning the crank at a slow and constant rate.
5. One person will read the Force Meter, and another will read the number of tick marks on the rope as it moves through the rope guide.  BE READY TO WRITE DOWN THE LARGEST READINGS ON THE FORCE METER before the block slips.
6. After some amount of time, the block will slip along the board.  DO NOT MOVE ANYTHING ESPECIALLY THE CRANK after the slip happens.  Record FAfter, FBefore, E, and M on the data sheet provided.
7. Repeat the experiment with modifications that you think might give you some more insight into the questions we are addressing in this lab. You can either do the same experiment over again, or design a somewhat different experiment using the information you gathered from your first trial.  You should do at least two trials.
Three Earthquake Prediction Models:

1.  Characteristic Earthquake Model: Stress builds up on a fault to the level of the fault strength*, the earthquake occurs, and stress is reduced to a level equal to the friction on the fault.
2.  Time-Predictable Earthquake Model: Assumes that fault strength is constant and that the fault will always rupture when the stress reaches the fault’s maximum stress capacity. Slip on the fault can vary with each event. Greater slip releases more energy and the recurrence time (time between slip events) is longer because those stresses need to build up once again.
3.  Slip-Predictable Earthquake Model: The fault does not rupture at the same stress each time, but always reduces the stress on the fault to the same stress level.

*fault strength = the ability of a fault to withstand stress without rupturing.

(From Hall-Wallace, 1998)

Plotting and Analyzing the Data:

Now that you’ve seen several models to use for predicting earthquakes, you will process and analyze your own data that you collected.

For this lab you will produce two graphs.

Plot I: Force in Newtons (Fbefore and Fafter) vs.   Event Number
1.   Does any part of your graph look similar to any of the earthquake predictions models?
2.   Which parts of your graph could be considered characteristic, slip-predictable, or time-predictable? Label them.
3.   Why do you think your data follows these patterns?
4.   Does your data follow any one model more than the others?

Plot II: Magnitude (Slip Distance)   vs. Difference in Force (Fbefore -  Fafter)
1.   Before you graph your data, predict what kind of relationship you think exists between these variables.
2.   Once you’ve graphed your data, describe the relationship between magnitude and the difference in force.
3.   Is this the kind of relationship you expected? Why?

Here is a sample analysis of the following two graphs (both examples of plot type I):

 Plot #1 – Example 1 (3 blocks 1011 g): Plot #1 – Example 2 (2 blocks 801g): 5-7, it appears characteristic 24-25, it appears characteristic 9-10, it appears time-predictable 17-19, it appears characteristic 11-12, it appears time-predictable 12-15, it appears characteristic 14-17, it appears time-predictable 8-9, it appears slip-predictable 22-24, it appears slip-predictable

Reflection Questions:

• Based on your experiment, what do you think influences when a blockquake occurs?
• Do you think there is a connection between any of the variables you recorded?  (For example, is there a relationship between mass and magnitude?)
• Working as a team, can you come up with a hypothesis about when a blockquake will occur and how big it will be?
• Test your hypothesis by doing another experiment. Was your idea right?  What was right about it, and what was wrong about it.
• Did your blockquakes occur randomly, or did they systematically depend on a particular variable you measured?
• What is the relationship between the amount of force on the blocks before the earthquake and after the earthquake?  Do you notice a pattern?
• Is this experiment a good model for how earthquakes really happen in the Earth?  Why or why not?
• Does the probability that the block will slip depend on what happened in previous slip events?
Reference:

Hall-Wallace, M. (1998), Can Earthquakes be Predicted?, Journal of Geoscience Education, 46, 433-443.