I’m guessing that most of you have, like me, spent at least some time in front of the screen these past few days absorbing the horrific images coming out of Japan. The most awesome—in the original sense of the word—visuals I’ve seen so far have involved water, but there are some pretty amazing pictures of split roadways and videos of skyscrapers swaying.
(I should mention that as I’m writing this, all of the news footage has been from Tokyo and other outlying areas. I haven’t yet seen pictures or videos of what happened in Sendai itself. I’m not looking forward to that; it’s sure to be terrible.)
Most of the death and devastation—at least until the Fukushima Daiichi plant melts down—has been caused by the tsunami which was, in turn, caused by the earthquake. Humans don’t yet have the technology to avoid or prevent the destruction caused by tsunamis. But the fact that an earthquake so powerful caused so little damage is a testament to how well the Japanese earthquake-proof their buildings. Those skyscrapers swayed; they didn’t fall down.
At 8.9 on the Richter scale, this was, if I remember correctly, the fifth-strongest earthquake ever recorded. The 2010 earthquake off the coast of Chile in 2010 was almost as strong, 8.8, while the one that destroyed Port-au-Prince, Haiti a month before that measured 7.0.
Now, some of you may be thinking something along these lines: Those are all pretty strong. Haiti was a 7, and the other two were basically 9s. There’s not a lot of difference there.
OK, it’s true that the difference between 7.0 (Haiti) and 8.9 (Japan) is 1.9. And an earthquake that measures 1.9 is too small to be felt. But that doesn’t mean that the difference between the Haiti earthquake and the Japan earthquake was too small to be felt. On the Richter scale, the difference between 7.0 and 8.9 is much, much, much greater than the difference between 0 and 1.9. Why? Because the Richter scale is logarithmic.
Y’know how when some number is growing by leaps and bounds, we say it’s increasing exponentially? That’s what the Richter scale does. Because it’s a logarithmic scale, and logarithms are exponential.
Boring Math Stuff
Skip this section.
A logarithm is, literally, an exponent. I don’t have the HTML capability on this blog to write exponents, or many other equation-related things either, and I don’t feel like doing them up as graphics and inserting them, so I’m going to have to explain this in words.
In the famous equation e equals m c squared, the little “2″ above the “c” is an exponent. It means, as I just said there, “squared,” or “raised to the second power,” or “multiplied by itself.” As another example, 3 raised to the second power is 3 x 3, or 9. Three raised to the third power is 3 x 3 x 3, or 27. Three raised to the fourth power is 3 x 3 x 3 x 3, or 81.
I decided to make graphics. Sue me.
In that equation on the left there, 3 is the base, 4 is the exponent, and 81 is … well … it’s … umm … I don’t think it has a name. It’s a number.
A logarithm is the exponent to which a base is raised in order to reach a number. I’m going without graphics on this one, but the equation would be spoken aloud as, “The logarithm of 81 to the base 3 is 4.” See how that corresponds to the shorter equation up there? The logarithm — 4 — is the exponent.
There are lots of logarithmic scales out there. For example, decibels. And star magnitudes. And the Richter scale. (I think I read somewhere that Richter based his scale on the stellar magnitude scale.) On a logarithmic scale, 2 is not twice as loud/bright/strong as 1, and 6 is not twice as loud/bright/strong as 3. Why? Because the numbers on the scale are logarithms. They’re exponents.
Which is useless information without knowing what the base is. It doesn’t help to know what power you’re raising a base to if you don’t know what the base is.
In the case of the Richter scale, the base is 10.
All Clear! Math Is Over!
Start reading again.
What that means is that each step on the Richter scale is 10 times greater than the one before it. An earthquake that measures 8.0 is ten times stronger than one that measures 7.0, and an earthquake that measures 9.0 is one hundred times stronger than one that measures 7.0. So Friday’s earthquake in Japan was almost 100 times stronger than the one in Haiti in 2010.
But Wait, There’s More!
What exactly is being measured on the Richter scale?
An earthquake occurs when parts of Earth’s crust move suddenly. That movement causes vibrations to travel through the earth. The vibrations are called seismic waves. Seismographs measure the amplitude—the height (or depth)—of those waves. That’s what’s tracked on the Richter scale.
The amplitude of this wave decreases over time.
This shows what amplitude—and a bunch of other things—look like on an actual simulated seismograph readout.
Look at the last sentence in the previous section up there. What it really should say is, “So Friday’s earthquake in Japan produced seismic waves that, when measured on a seismograph, were almost 100 times taller and 100 times deeper than the waves produced by the earthquake in Haiti in 2010.”
That’s nice, but not very helpful. Well, OK, it’s helpful on an intellectual level. It gives us a good basis for comparison. But it doesn’t let us really know what the earthquake would have felt like.
Instead, let’s talk about energy. One of the standard textbook definitions of energy is “the ability to cause movement or change.” So let’s talk about how much movement of the earth and change in the landscape Friday’s earthquake caused. Turns out that each step on the Richter scale corresponds to a 3100% increase in the amount of energy released. In other words, an earthquake that measures 8.0 releases 31 times more energy than one that measures 7.0, and an earthquake that measures 9.0 releases 31 x 31, or 961 times more energy than one that measures 7.0. So Friday’s earthquake in Japan released almost 961 times more energy than the one in Haiti in 2010.
Absolute Terms
It’s not really helpful to compare one earthquake to another if you weren’t in either one of them. And besides, the Haiti earthquake was pretty darned powerful. So what can we do?
We want to compare energy release. What releases a lot of energy in ready-measured amounts? Bombs. Let’s look at them.
The atomic bomb dropped on Hiroshima released as much energy as a 6.0-magnitude earthquake. Friday’s earthquake released roughly 25,000 times more energy than that.
That’s not really fair, because the Hiroshima bomb was crude my modern standards. First of all, it was a fusion bomb, not a fission bomb. So let’s look at fission bombs, or “H-bombs.”
Hydrogen bombs come in all different sizes. But an average one might release as much energy as a 7.0-magnitude earthquake. Friday’s earthquake released nearly 961 times more energy than that.
Think about that for a minute. Picture dropping 900 hydrogen bombs all at once on the same spot off the coast of Sendai. I can’t even imagine it. But in a sense, that’s what happened.
Thanks for ‘splaining, Bruce! Did I actually read somewhere that the whole country moved 8 feet because of the quake?
Hey, Tricia. I can’t speak to what you did or didn’t read, but the way I understand it, the east coast of Honshu moved 15 feet to the east. So Japan is now 15 feet wider and 15 feet closer to the U.S. than it used to be. Cool, huh?
Also it would really help if you could explain a bit about the radiation risk…I found this http://xkcd.com/radiation/ and now I’m a little frightened by bananas!
I’d thought about doing that, but it’s a really big topic. And given that the situation in Fukushima is changing daily, there are other sites out there better equipped for the task. One source for informed and comprehensible articles is IEEE Spectrum Online. It’s written by engineers, so there’s no political bias one way or the other. I’m sure there are other good sites out there as well.
I’m…uhh…I’m going to assume you’re joking about the bananas, given that the whole point of that infographic was too show minuscule, quotidian, and non-threatening some levels of exposure are.