This is a frequency magnitude plot of every earthquake in the world that happened in 2007 that made it into the USGS catalog. And what we are plotting here is magnitude on the x axis and the cumulative number of earthquakes greater than or equal to that magnitude on the y axis. So these are log log axes. You can see here that each gradation is a power of 10. Magnitude is actually already a power of 10 because a magnitude 5 earthquake is 10 times bigger than a magnitude 4. So this is log log. The relationship follows approximately this equation here. The log of the number of earthquakes exceeding some magnitude is equal to a minus b times that magnitude. a is the y intercept, b is a slope. In practice, b is usually about 1. What I can do is draw a line on here to show you what I’m talking about. There’s a line with a slope of negative 1. I am not fitting the data here, I am just drawing it on there. This relationship only holds true for the part of the catalog that is complete. Catalogs can be incomplete in two ways. One way is by magnitude threshold. You can see that below about magnitude 4 not every earthquake in the world is getting recorded by the USGS. That is why this green line flattens out here even though the real relationship should keep going up. At the high end you are limited in time. This catalog is only one year long. If it were one hundred years long then this green line would follow along for longer but instead it peters out right here.