In this little video I am going to explain how earthquake recurrence interval can be extrapolated from seismic catalog data. In this plot the x axis is magnitude and it is going from zero to six. The y axis is mean number of events per year greater than or equal to some magnitude. It extends from ten to the minus two up to one thousand. The red curve is data. It is a thirty year catalog from the New Madrid Seismic Zone. I have normalized it to just one year. We can read this plot and see how many earthquakes of different magnitudes happen every year. So for example if we want to know how many magnitude threes happen every year we can just look right here. This is where three is so we can look on the y axis. This is a log log plot so this is one,  two, three, four. What this means is that there are four earthquakes every year that are at least as big as magnitude three. How many magnitude fives happen every year? We can read this off the plot. Right here is ten to the minus two so that is point zero one, two, three, four, five, six, seven. There are about point zero seven magnitude fives that happen every year. That is kind of hard to think about. But with simple arithmetic we can realize that if you have point zero seven earthquakes in one year, that is the same thing as saying there is one earthquake every fourteen point three years. So that is nice. Now how many magnitude sixes happen every year? Unfortunately, our thirty year catalog did not even include one magnitude six so that means we have to extrapolate. Let us make our axes bigger so we have a clue about what we are doing here. Now I have extended the x axis from zero to nine and I have made the y axis go from one thousand down to ten to the minus five. If we want to know how many sixes, sevens, eights, and nines there are in this region what we really need to do is extend this curve down as if this data were here. We could spend a lot of time discussing how to best fit this data but I am not going to do that right here, instead I am just going to slap a fiducial line whose slope is negative one right on there. There is my line. I think that fits the data pretty well actually. How many magnitude eights happen every year? Not very many. This is ten to the minus five. So this is two, three, four, five times ten to the minus five magnitude eights happen every year and this is the same as saying one magnitude eight every twenty thousand years.