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.
For instance; 102 100 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 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 TNT for Seismic Example
Magnitude Energy Yield (approximate)
-1.5 6 ounces Breaking a rock on a lab table
1.0 30 pounds Large Blast at a Construction Site
1.5 320 pounds
2.0 1 ton Large Quarry or Mine Blast
2.5 4.6 tons
3.0 29 tons
3.5 73 tons
4.0 1,000 tons Small Nuclear Weapon
4.5 5,100 tons Average Tornado (total energy)
5.0 32,000 tons
5.5 80,000 tons Little Skull Mtn., NV Quake, 1992
6.0 1 million tons Double Spring Flat, NV Quake, 1994
6.5 5 million tons Northridge, CA Quake, 1994
7.0 32 million tons Hyogo-Ken Nanbu, Japan Quake, 1995; Largest thermonuclear weapon
7.5 160 million tons Landers, CA Quake, 1992
8.0 1 billion tons San Francisco, CA Quake, 1906
8.5 5 billion tons Anchorage, AK Quake, 1964
9.0 32 billion tons Chilean Quake, 1960
10.0 1 trillion tons (San-Andreas type fault circling Earth)
12.0 160 trillion tons (Fault Earth in half through center,
OR Earth's daily receipt of solar energy)
1. According to the table what magnitude earthquake releases a similar amount of energy to small
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
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
10. Using either your graph or the table write an exponential equation that gives the energy yield for any
11. An earthquake has a seismic energy release of approximately 500 billion tons. About what magnitude
earthquake was this?
Created by YUMMYMATH.com