## Earthquake Magnitudes and the Gutenberg Richter Law

In order to study the noise of earthquakes, we must first find a way to measure the sizes of earthquakes. Charles Richter developed the main scale that is used today. On the Richter scale, the magnitude (M) of an earthquake is proportional to the log of the maximum amplitude of the earths motion. What this means is that if the earth moves one millimeter in a magnitude 2 earthquake, it will move 10 millimeters in a magnitude 3 earthquake, 100 millimeters in a magnitude 4 earthquake, and 10 meters (33 feet!) in a magnitude 6 earthquake. So when you hear about a magnitude 8 earthquake and a magnitude 4 earthquake, you now know that the ground is moving 10,000 times more in the magnitude 8 earthquake than in the magnitude 4 earthquake. The difference in energies is even greater. For each factor of 10 in amplitude, the energy grows by a factor of 32, so a magnitude 8 earthquake releases 1,000,000 times more energy than a magnitude 4 earthquake. It is no wonder they do so much more damage!

## The Gutenberg-Richter Law When people started measuring the magnitudes of earthquakes, they found that there were a lot more small earthquakes than large ones. On the right, you can see a plot of all the earthquakes of magnitude 4 or greater in 1995. You can see that there are a few really big earthquakes, and many many small earthquakes. Geologists have found that the number of earthquakes of magnitude M is proportional to 10-bM. They call this law the Gutenberg-Richter law. Look at the graph of all the earthquakes in 1995 on the left: the red line gives the Gutenberg-Richter prediction with b = 1. The value of b seems to vary from area to area, but worldwide it seems to be around b=1.  