Matt Yglesias writes that he “hear[s]” the Chilean earthquake is 1000x more powerful than the Haitian one. I get the feeling that a lot of people know that the Richter scale is logarithmic, but it’s not clear that they always know how to convert that back into raw units. The estimable Mr. Yglesias, for instance, shouldn’t need to “hear” that it’s 1000x more powerful; he should be able to figure it out on his own. (I get similarly vexed when people can’t compute tips at restaurants on their own.)
Seismologists indicate the size of an earthquake in units of magnitude. There are many different ways that magnitude is measured from seismograms because each method only works over a limited range of magnitudes and with different types of seismometers. Some methods are based on body waves (which travel deep within the structure of the earth), some based on surface waves (which primarily travel along the uppermost layers of the earth), and some based on completely different methodologies. However, all of the methods are designed to agree well over the range of magnitudes where they are reliable.
Preliminary magnitudes based on incomplete but available data are sometimes estimated and reported. For example, the Tsumani Centers will calculate a preliminary magnitude and location for an event as soon as sufficient data is available to make an estimate. In this case, time is of the essence in order to broadcast a warning if tsunami waves are likely to be generated by the event. Such preliminary magnitudes, which may be off by one-half magnitude unit or more, are sufficient for the purpose at hand, and are superseded by more exact estimates of magnitude as more data become available.
Earthquake magnitude is a logarithmic measure of earthquake size. In simple terms, this means that at the same distance from the earthquake, the shaking will be 10 times as large during a magnitude 5 earthquake as during a magnitude 4 earthquake. The total amount of energy released by the earthquake, however, goes up by a factor of 32.
So then the amount of shaking in a magnitude-7.0 earthquake is 107, which is 10 million. A magnitude-8.8 earthquake will feature 101.8 times as much shaking as the magnitude-7.0 one. 101.8 is less than 102, which is 100. So the amount of shaking is nowhere near the 1000x that Mr. Yglesias heard.
But then the USGS also notes that the amount of energy goes up by a factor of 32 for every 1-unit increase in the Richter scale. So then there’s 321.8, or 512x, as much energy in a magnitude-8.8 earthquake as in a magnitude-7 one.
P.S.: I found an Ezra Klein piece that I was looking for before, where he suggests that he also doesn’t know what “logarithmic scale” means:
The devastation in Haiti was not just because the earth shook, and hard. The quake there was 7.0. Harder than the 6.5 quake that hit Northern California a day before (remember, though, that the Richter scale is logarithmic, so 7 is many times harder than 6.5)
If we’re talking about the magnitude of the shaking, the Haiti quake was 10.5 times as strong as the California one. You may remember that “x to the 0.5 power” is the same as “the square root of x.” To get your back-of-the-envelope-math muscles working, recall that “the square root of x” means “the number which, when squared, equals x.” The square of 3 is less than 10, and the square of 4 is more than 10, so the Haiti quake shook things somewhere between 3 and 4 times as hard as the California quake. As measured by raw power, Haiti’s quake was 320.5 times as powerful as California’s, meaning somewhere between 5 and 6 times as powerful.
“Many” has no exact definition, of course, but I doubt most people would say that “many times harder” means “between 3x and 6x as hard.”