Earthquakes and Richter Magnitude
Name
_______________________________
On Tuesday, August 23, 2011, two sizable earthquakes occurred in the US. One was in Colorado
with a magnitude of 5.3 and the other was centered in Virginia with a magnitude of 5.8 … which we
felt here in Massachusetts.
Seismologists view images on seismographs like this image on the right from
Tuesday’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.
101  10
For instance; 102  100
The exponents 1, 2, and 1.7 are the base-10 logarithms of 10, 100, and 50.12.
101.7  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 recent U.S. 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)
-1.5
1.0
1.5
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
12.0
6 ounces
30 pounds
320 pounds
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
160 trillion tons
Breaking a rock on a lab table
Large Blast at a Construction Site
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)
(Fault Earth in half through center,
OR Earth's daily receipt of solar energy)
Questions:
1. According to the table what magnitude earthquake releases a similar amount of energy to small
nuclear weapon?
2. Approximately how many tons of energy was released during the August 23, 2011 earthquake off
centered in Virginia?
3. Approximately how many tons of energy was released during the March 11, 2010 earthquake off of
Japan? (8.9 on the Richter scale)
4. According to the chart, how many times greater is a 5.0 magnitude quake than a 4.0 magnitude
quake?
5. According to the chart, how many times greater is an 8.0 magnitude quake than a 7.0 magnitude
quake? How many times greater is a 9.0 magnitude quake than an 8.0 magnitude quake? See any
patterns? Does this pattern hold roughly true in the table?
6. Using the information from the table create a graph that gives the energy yield for any Richter
magnitude. Put Richter magnitude on the x-axis and put energy yield on the y-axis.
7. Approximately how many tons of energy was released during the 2010 earthquake in Haiti (7.1)?
8. Approximately how many tons of energy was released during the 2010 earthquake in Chile (8.8)?
9. Approximately how many tons of energy was released during the 1906 earthquake in San Francisco
(7.9)?
10. Using either your graph or the table write an exponential equation that gives the energy yield for any
Richter magnitude.
11. An earthquake has a seismic energy release of approximately 500 billion tons. About what magnitude
earthquake was this?
Created by YUMMYMATH.com
Sources: http://crack.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html
http://en.wikipedia.org/wiki/Richter_magnitude_scale