How Much Bigger is a 4.7 Earthquake Than a 4.4? Twice As Big.
OMG it’s a math post!
Yesterday we had an earthquake here in SoCal. It was the most dramatic one I’ve been here for, by a long shot, and my friends have all said the same � probably because we all live near the epicenter and it was quite a shallow quake.
It turned out the earthquake � a bit of a disappointing number after what we had felt! Anyway, it was first reported in as a 4.7, and then revised to a 4.4, and someone retweeted this tweet:
�: Just heard from our son in LA. Status downgraded from 4.7 to 4.4. You know how much difference that makes.� Uh, .3???
� Ron Perlman (@perlmutations)
Well, yeah. But that doesn’t really tell us anything, does it? It’s a difference of .3 on the Richter scale, but the Richter scale is logarithmic, and we silly humans aren’t used to thinking in logarithms unless we’re astronomers. So how much bigger IS a 4.7 than a 4.4?
(cut for math)
Here’s the way : seismologists measure the “shaking amplitude� (how big the waves on the seismograph are) and compare it to a smaller wave. For the purposes of this (simplified) post, I’m going to call that number how “big� the earthquake is. Then, to get the Richter scale number, you take the base ten logarithm of that number.
In practical terms, the logarithmic scale means that every number you move up on the Richter scale is ten times bigger than the previous number. A 5.0 earthquake is ten times bigger than a 4.0. A 6.0 earthquake is a hundred times bigger than a 4.0. A 7.0 earthquake is a thousand times bigger than a 4.0.
So how much bigger is a 4.7 than a 4.4? Well, how “big� is the 4.7? Let’s say X. How “big� is the 4.4? Let’s say Y. Then we have the following relationships:
To find out how much bigger the 4.7 was than the 4.4, let’s subract and use some handy log rules:
Convert to exponential form:
So the earthquake with strength X is 1.9953 times bigger than the earthquake with strength Y. In other words, a 4.7 is twice as big as a 4.4!
How much energy it releases is a whole ‘nother ball of wax, from what I understand.
