Earthquakes and Richter Magnitude
Name
_________________________
Recently Northern Chili and Los Angeles, California have experienced powerful earthquakes and aftershocks. Seismic activity is
expected to continue.
Seismologists view images on seismographs like this image on the right from Chili’s earthquake. They calculate the vertical distance between
the extremes on this image and call that the amplitude of the shake.
The Richter Magnitude of the earthquake is the base-10 logarithm of that amplitude. Logarithms are related to exponents. Base-10 logarithms
are the exponent required to bring 10 to a certain number.
For instance; 10! = 10
10! = 100
10!.! = 50.12
The exponents 1, 2, and 1.7 are the base-10 logarithms of 10, 100, and 50.12.
Seismologists use a Richter Magnitude scale to express the seismic energy released by an earthquake. The Richter Magnitude scale is a
logarithmic scale representing the amplitudes of the seismograph reading. The chart below demonstrates Richter magnitude numbers and the
explosive equivalent of energy that the magnitude represents.
Let's take a look at the seismic wave energy yielded by our two examples of recent activity and compare those to earthquakes and other
phenomena. For this we'll use a larger unit of energy, the seismic energy yield of quantities of the explosive TNT:
Richter
Magnitude
TNT for Seismic
Energy Yield
Example
(approximate)
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
10.0
1 ton
4.6 tons
29 tons
73 tons
1,000 tons
5,100 tons
32,000 tons
80,000 tons
1 million tons
5 million tons
32 million tons
160 million tons
1 billion tons
5 billion tons
32 billion tons
1 trillion tons
Large Quarry or Mine Blast
Small Nuclear Weapon
Average Tornado (total energy)
Little Skull Mtn., NV Quake, 1992
Double Spring Flat, NV Quake, 1994
Northridge, CA Quake, 1994
Hyogo-Ken Nanbu, Japan Quake, 1995; largest thermonuclear weapon
Landers, CA Quake, 1992
San Francisco, CA Quake, 1906
Anchorage, AK Quake, 1964
Chilean Quake, 1960
(San-Andreas type fault circling Earth)
1. Look at the table. What do you see? What do you think? What does it make you wonder?
Kids might see destruction, that the power between magnitudes increases a lot, much more than a linear function. They might cite
examples of destruction. They might think about the power of a 1.0 or an 11.0. They might think this scale doesn’t really communicate the
difference in power between earthquakes. They might wonder what type of algebraic relation is demonstrated in the table.
2. How would you describe the change in destructiveness as you move up in Richter magnitude? Is the relationship between magnitude and
energy yield roughly proportional? Linear? Something else? Discuss your reasoning.
It is exponential.
3. Lets find the multiplicative difference between one Richter magnitude. Use the table to answer the following questions:
a. How many times greater is a 3.0 magnitude quake than a 2.0-magnitude quake?
X 29
b. How many times greater is a 4.0 magnitude quake than a 3.0-magnitude quake?
X 34.5
c. How many times greater is a 5.0 magnitude quake than a 4.0-magnitude quake?
X 32
d. How many times greater is a 6.0 magnitude quake than a 5.0-magnitude quake?
X 31.25
e. How many times greater is a 7.0 magnitude quake than a 6.0-magnitude quake?
X 32
f. How many times greater is an 8.0 magnitude quake than a 7.0-magnitude quake?
X 31.25
g. How many times greater is a 9.0 magnitude quake than an 8.0-magnitude quake?
X 32
h. How many times greater is a 10.0 magnitude quake than a 9.0-magnitude quake?
X 31.25
4. Look back at your answers from problem three. What pattern do you notice? About how much more powerful is an earthquake when we
move up one unit on the Richter scale? How about when you move up two units on the scale?
It’s about 31.6 times greater when you move up the scale 1 unit and when you move up the scale two units it is about 1000 times
greater.
5. How powerful do you think a 12.0 magnitude quake would be?
1,000 times greater than a trillion tons.
6. Do you think a more powerful earthquake necessarily translates to a more destructive earthquake? For example, will a 6.0 earthquake
always cause more damage than a 5.0 earthquake?
No, it depends where the earthquake is located, such as a city or rural area. If nothing is there, then there is less “stuff” to be damaged.
7. The graph below shows the energy yield for Richter magnitudes from 2.0 to about 5.0. Notice that the graph is not linear. Follow the curve
to find the energy yields from a 4.3 magnitude earthquake. Do the same for a 4.7 magnitude earthquake.
A 4.3 is an energy yield of about 2,000 and a 4.7 is about 8,000.
This is the equation that our Excel graph gave us when we eliminated magniturde 1 and 1.5 from the data used to graph the equation.
y = 0.0008e3.4693x
Excel shows logarithmic trend graphs as natural logs. To change the natural log to the base 10 log, we did this mathematics;
ln 𝑥
3.4693
=
= 1.5067
ln 10 2.302585
y=0.0008 * 10^(1.5067x)
8. If you had to create a create a graph showing the relationship between Richter magnitude and energy yield what scales would you use
your for your graph? Take some time to discuss this in small groups or as a class. What are the difficulties of graphing all of this data on
one graph?
This is difficult. You can graph it, but then it is not very useful for finding specific values, unless you create a graph the size of a wall.
9. Using the information from the table create a graph that gives the energy yield for any Richter magnitude. This might be pretty hard to
graph. Consider graphing a small range of Richter magnitudes such as magnitudes of 2 to 5 or 3 to 6 or 6 to 9 to graph. Perhaps as a
class you will have all data graphed between three different graphs.
We’ve shown the graph of magnitudes 3 to 5 in problem # 7 and above is the zoomed out graph of magnitudes 5 to 7. Notice that the Yaxis values on this last graph are much greater intervals than on the magnitude 3 to 5 graph in problem #7.
10. Use the graphs you created in class to find approximately how many tons of energy was released during the 2010, 7.1 earthquake in Haiti.
About 10 million tons
11. Use the graphs you created in class to find approximately how many tons of energy was released during the 2014, 8.2 earthquake in Chile.
About 10 billion tons
12. Use the graphs you created in class to find approximately how many tons of energy was released during the 2014, 5.1 earthquake in L.A.
About 34,000 tons
13. Use the graphs you created in class to find approximately how many tons of energy was released during the 1906, 7.9 earthquake in San
Francisco.
About 300 million tons
14. An earthquake has a seismic energy release of approximately 500 billion tons. About what magnitude earthquake was this? How did you
find it?
About 9.4-magnitude
15. Using either your graphs or table write an exponential equation that gives the energy yield for any Richter magnitude. Consider either
roughing out an equation that fits the data, or use technology (such as Excel, Desmos or Geogebra) to give a more precise equation.
𝑦 = 32(!!!)
Or 𝑦 = .00096(31.86) !
Or maybe 10 ! = 32 ∗ 𝑋
Created by YUMMYMATH.com Sources:
http://crack.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.htmlhttp://en.wikipedia.org/wiki/Richter_magnitude_scale