## Sunday, November 2, 2014

### NEGATIVE Earthquake Magnitudes?

Some questions require an explanation of a different kind of number that some students haven't yet seen before. These different ways of expressing numbers were developed to help explain very large things, very many things, very small things, or very complex things, among others.

Q: Hi, My name is Anthony. I was wondering how negative magnitudes can be recorded for earthquakes, and what is the smallest earthquake ever measured? Thanks
- Anthony N

A: Earthquake magnitudes are actually exponentials, so a negative exponential doesn't mean a "negative" value in the usual sense of the word. I'm hoping you've already had exponentials in school - or at least you can go ask a teacher what they are.

For instance,
10(exp)+2 = 10^+2 = 100.0
The exponent here is +2 and it means one hundred. This is 10 to the second power.
10(exp)+1 = 10^+1 =   10.0
The exponent here is +1 and it gives ten - ten to the first power.
10(exp) 0  =  10^0   =     1.0
The exponent here is 0 and it means one - ten to the zeroth power.
10(exp)-1  =  10^-1  =     0.1
The exponent here is a negative number, but it refers just to a SMALLER value than a non-negative exponent would. Here ten to the minus first power means one tenth.

The smallest earthquake ever recorded is a bit more difficult to answer. There are three parts to the answer:

1. It depends on the sensitivity of the instrument, and how close the hypocenter of the earthquake (the actual rupture point) is to the instrument. There are a lot of sensitive seismometers set up around the world as part of the global seismic network - they are designed to look for earthquakes in the magnitude 2 range or higher. There are also some really, really sensitive seismometers positioned on and around volcanoes. These are set up to look for earthquakes so tiny that earthquake people wouldn't really be interested in them - events so small that only one or two of the nearby instruments may even detect them, and no human would likely feel them.

2. I believe that the smallest recorded events are probably in the M= -2 range (negative two magnitude) for a very clean, noise-free station. That's also what two seismologists in my office tell me (independently!).

3. When you are looking at magnitudes this small, you are also dealing with a lot of noise: cars driving by on a nearby highway, people or animals walking nearby, wind vibrating trees and buildings, etc. In a sense, the smallest earthquake ever recorded is sort of meaningless, because it becomes harder and harder to even know if it's real - or just noise. Also, the smaller the seismic events, the more common they are. As an example, the US Geological Survey estimates that there were about 1,300,000 earthquakes worldwide in the 2.0 - 2.9 magnitude range. There are MANY more as you get to ever smaller magnitudes. See an earlier chapter on how many earthquakes are detected each year in each magnitude range (http://askageologist.blogspot.com/2012/11/earthquakes-how-often.html).

No one is really interested in most of the wiggles you see in these two examples: